A point charge is an idealized model of a particle which has an electric charge. A point charge is an electric charge at a mathematical point with no dimensions.
The fundamental equation of electrostatics is Coulomb's law, which describes the electric force between two point charges. The electric field associated with a classical point charge increases to infinity as the distance from the point charge decreases towards zero making energy (thus mass) of point charge infinite.
Earnshaw's theorem states that a collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges.
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